Abstract: Constructive reasoning has an established place within mathematics, philosophy, and computer science. It can feel more comfortable, and be easier to see what's valid and what's not, if one has access to semantics for such a system. While several are well-known, in this talk I will develop topological models. Analogous to forcing in set theory, topological models give a natural way of providing independence proofs in many important cases. I will give a general description of them and illustrate it with a host of examples.